Asmussen, whose family operates a training center in Texas and whose brother, Cash, was a successful jockey in Europe, began his career in racing as a jockey at age 16. After riding in New Mexico, California, and New York, for three years, Asmussen was unable to continue in the saddle because his height and weight precluded him from being able to continue.

In 1986, Asmussen began training Thoroughbreds and Quarter Horses. He was voted an Eclipse Award for outstanding training in 2008.

Among the best horses trained by Asmussen have been two-time Horse of the Year Curlin and Rachel Alexandra, who was also honored as Horse of the Year.